Question: Suppose that $wz = 12-8i$, and $|w| = \sqrt{13}$.  What is $|z|$?
Explanation: Since $wz = 12-8i$, we have  \[|wz| = |12-8i| = |4(3-2i)| = 4|3-2i| = 4\sqrt{3^2 + (-2)^2} = 4\sqrt{13}.\]Since $|wz| = |w|\cdot |z|$, we have $|w|\cdot |z| = 4\sqrt{13}$.  Finally, since we are given that $|w| = \sqrt{13}$, we have $|z| = \boxed{4}$.